mine sounds exactly the same as this (1997 EDC 300tdi auto). Its been like this as long as I've had it, around 10 years. I have replaced the sender unit, fuel line (got rid of the sedimenter and ran a fuel line straight through), put a 1 way valve before the new Delphi lift pump. The fuel filter is replaced every 3000 miles with a Mann filter. I recently fitted a new 3.2 ohm cold weather environment starter motor, spins faster than the old, original, one, but doesn't start any quicker. Also have a 1000CCA Marine battery fitted. I have new glow plugs but the ones that are there seem to check out ok, so not yet fitted. This poor starting is not weather dependent as it is exactly the same whether its 30 degrees or -10. Doesn't blow smoke when its running and I have always had "this goes well" comments from anyone that's driven it. As the OP says its just !st start of the day, or if its allowed to go cold again. When the engines warmed up, no problem. There doesn't seem to be any fuel leaks (or air).
Very frustrating. I did try the by pass of the temp sensor in the head, with a 7.5 ohm resistor, and that seemed to be better but I have always shied away from lecktrickery (colour blind), so not sure how to do a permanent switch.
It has always been a bit of a joke with the kids and the missus, with calls of "come on Landy" every time we went anywhere. But I have to admit its wearing a bit thin now.
Apologies to the OP for the long ranting post/reply, just showing that your never on your own with whatever Land Rover problem you have.